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In broadband phased arrays, the elements near the edges have a widely deviating behavior. This is analyzed here with the help of a finite-by-infinite array approach. The solution of the equations is dramatically accelerated by decomposing the array into two approximate semi-infinite arrays (APSIAs), the solution of which is obtained recursively for arrays of increasing size. For very large arrays, the solution is extrapolated further inside the array by using a model for the waves scattered by the edges of the array. Simulations results are shown for arrays of tapered-slot antennas in receiving conditions.